A counter-example to Birkhoff's theorem?

Suppose that we have a symmetric shell of matter which is kept static by support props of some kind. Both the mass, and the pressure in the props is a source of the gravitational field.

Release the props. The pressure disappears. The gravitational field weakens?

If pressure would not be a source of the gravitational field, then we could build a perpetuum mobile from uncompressible fluid. Put such fluid in a rigid vessel. Use a gravitational field to curve the space inside the vessel, so that we can pump a little more of the fluid inside. Remove the gravitational field. We obtain an infinite pressure inside the vessel.

Note that we cannot change the gravitational pull of a vessel just by putting pressure to it. The reason is that the negative pressure in the walls of the vessel cancels out the positive pressure inside the vessel.

Besides the pressure, also the momentum contributes to the stress-energy tensor. We only can remove the pressure in a prop at the speed of light. Meanwhile, the momenta of particles in the shell starts to grow. Probably the change in the momenta balances the lost pressure, so that the field stays constant. This is not a counter-example.

Also, if the prop is made of ideal gas in some container, then opening the container will convert pressure (the kinetic energy of atoms) to momentum.

A black hole from an expansion of massive shell and a collapse of a less massive shell?

Let us make a massive spherical shell to expand rapidly by some mechanism. Let us collapse a less massive shell on it, so that the system for a brief time is inside the Schwarzschild radius for the combined mass-energies.

Let us assume that the shells pass through each other with no interaction. Can the massive shell climb above the Schwarzschild radius?

It cannot, if the metric is smooth. Above the Schwarzschild radius, the past light cone of an observer contains just events above the Schwarzschild radius => he will construct his local metric purely based on the events above the horizon. Similarly, the future light cone of any event just below the horizon is completely below the horizon.

But the future light cone in the Minkowski space does contain points that are farther away from the center. The upper surface of the shell cannot move up. The lower surface may move up. What happens? The shell is squeezed how much?

Infinite pressure in a collapsing mass shell?

In the collapse of a shell, the gravitational pull on the lower surface of the shell is zero, while the pull on the upper surface grows infinite at the event horizon. The pressure becomes infinite. Does this show that we cannot extend the Schwarzschild metric past the event horizon? In the Penrose diagram, the surface of the star passes through the horizon.